The anisotropic maximal function is defined by means of one-parametric parallelepipeds instead of cubes. For vector-valued anisotropic maximal functions there are proved weak and strong type weighted inequalities. The strong type inequality is then utilised in the proof of an anisotropic weighted mixed norm maximal inequality.
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Vakhtang Kokilashvili, Jiří Rákosník, Weighted Inequalities for Vector-Valued Anisotropic Maximal Functions. Z. Anal. Anwend. 4 (1985), no. 6, pp. 503–511DOI 10.4171/ZAA/170